Beginning of Essay
At the end of the fifteenth century, celestial navigation was just being developed in Europe, primarily by the Portuguese. Prior to the development of celestial navigation, sailors navigated by "deduced" (or "dead") reckoning, hereafter called DR. This was the met ....

Middle of Essay
.... the vessel (in miles per hour) by the time traveled to get the distance. In Columbus's day, the ship's speed was measured by throwing a piece of flotsam over the side of the ship. There were two marks on the ship's rail a measured distance apart. When the flotsam passed the forward mark, the pilot would start a quick chant, and when it passed the aft mark, the pilot would stop chanting. (The exact words to such a chant are part of a lost oral tradition of medieval navigation). The pilot would note the last syllable reached in the chant, and he had a mnemonic that would convert that syllable into a speed in miles per hour. This method would not work ....